{"title":"General Right-Sided Orthogonal 2D-Planes Split Quaternionic Wave-Packet Transform","authors":"Hakim Monaim, Said Fahlaoui","doi":"10.1007/s00006-023-01303-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.\n</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01303-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.
期刊介绍：
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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